Best Known (54, 54+79, s)-Nets in Base 9
(54, 54+79, 84)-Net over F9 — Constructive and digital
Digital (54, 133, 84)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 41, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (13, 92, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (2, 41, 20)-net over F9, using
(54, 54+79, 88)-Net in Base 9 — Constructive
(54, 133, 88)-net in base 9, using
- 2 times m-reduction [i] based on (54, 135, 88)-net in base 9, using
- base change [i] based on digital (9, 90, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- base change [i] based on digital (9, 90, 88)-net over F27, using
(54, 54+79, 182)-Net over F9 — Digital
Digital (54, 133, 182)-net over F9, using
- t-expansion [i] based on digital (50, 133, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(54, 54+79, 3242)-Net in Base 9 — Upper bound on s
There is no (54, 133, 3243)-net in base 9, because
- 1 times m-reduction [i] would yield (54, 132, 3243)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 915856 602550 076121 575353 653826 987190 581692 522807 115026 966890 407372 333074 197739 554236 533777 862743 704027 265606 028128 078686 597865 > 9132 [i]